Accounting for Teammates Part 1: Corsi Rel and WOWY

Jared Lunsford
July 18 2012 05:56PM



The quality of teammates influences almost every stat in all major sports. This is particularly true of the base stats we tend to use, such as on-ice Corsi or Fenwick rate, because they don't just take something a player has done (score a goal) but also include what his teammates did while he was on the ice. The reason we opt for on-ice stats instead of individual is simple - on-ice stats allow us to measure, albeit noisily, all the contributions a player makes to the thing you are measuring.

How often do you hear an announcer say "that kind of play doesn't show up on the stat sheet, but was very important"? If you're measuring on-ice stats instead of individual stats, and you have a large enough sample, those small plays will show up. The trick is accounting for teammate quality, or at the very least taking it into consideration.


The first thing one should recognize is that it's often difficult or even impossible to separate out guys that spend the majority of their time together. The Sedins are an obvious example, but it is very common for a top defense pairing to stick together most of a season and somewhat common for pairs or even entire lines of forwards to play the vast majority of their time together.

It all comes down to sample size. With apologies to Nashville fans in mourning, consider Shea Weber and Ryan Suter last season. Going by hockey analysis, at 5-on-5 they spent 1,293 minutes together, Suter played just under 213 minutes without Weber and Weber played almost 195 minutes without Suter. So they each played roughly 3 games' worth of time apart. With a sample size that small, we can't say much of anything.

Any team can look good or terrible over a three-game stretch. Last year Weber did substantially better when they were apart, but to figure out if one was driving play more than the other you would need several seasons' worth of data and even then it's just going to be a rough idea because those two spent so much of their time together.

A First Attempt - Relative Corsi

The most well known and, unfortunately, most widely used method of dealing with teammates is relative Corsi (Corsi Rel). To calculate relative Corsi, you simply take the possession rate when the player is on the ice and subtract off the possession rate when he is off the ice. The idea, broadly speaking, is that if a player is helping his team then, they will be better off with him on the ice than off. That's a fine idea but I have to say I'm not a fan of this metric at all. I'd love for someone to defend it in the comments because it puzzles me that it is ubiquitous given its major flaws. My intuition is that zone-start adjusted Corsi and maybe even just raw Corsi are better metrics than Corsi Rel.

Fellow Driving Play and NHLnumbers blogger Brent Morris provided a nice article of criticisms. In fairness, one could argue that a lot of the problems are down to misuse. Corsi Rel doesn't really adjust for teammates so much as say how your line/pairing does compare to the others on your team. The adjustment, subtracting off the team's Corsi when you are off the ice, puts most of the weight on the guys the player in question never plays with. If you are a first-pairing defensemen, it's mostly going to be determined by how well the second and third pairings go.

What we'd like to do is see how much credit we should give a player versus the teammates he plays with, and Corsi Rel does that very poorly.

A Step Up - WOWY

WOWY, an acronym of "with or without you", is a pretty substantial improvement. In the basic version, one compares how each teammate does with a player on the ice to his results without that player. The idea is the same - if you are good, you will make your teammates better. If a guy is improving his line/pairing then the other player(s) will be better with him than without him.

WOWY adjusts for teammates (or teammate at least) by holding them constant. If you look at Crosby's performance with and without Pascal Dupuis, Crosby will appear on each side of that. This is a big improvement on Corsi Rel because if Dupuis spends a lot of time with Crosby, Sid would mostly be in the Corsi On part which would elevate Dupuis's numbers.

One big issue with WOWY is that you can still get a dragged-along-by-teammate effect if you aren't careful. If you look at a Vancouver defenseman's Corsi with and without Alex Burrows he will be drastically better with Burrows on the ice. Burrows may be a good possession player but as pointed out above it's tough to say since he spent so much time with the Sedins; so it seems likely that a healthy share of the credit there should go to Henrik and Daniel. For this reason it is generally best to run WOWY numbers against teammates on the same color line - forwards with forwards and defensemen with defensemen. If you run it on a defenseman for a forward or vice-versa the results will be very similar to Corsi Rel and carry all those problems.

It's beyond the scope of this article, but you can do more fancy versions of WOWY by looking at combinations of players. For example, you could look at Pittsburgh's Corsi rate with and without Dupuis when both Crosby and Letang were on the ice. This allows you to take into account the quality of both forward and defensemen. The downside is that you are going to shrink the sample sizes pretty dramatically so you might have to go to multiple seasons, which can cause its own problems.

Final Thoughts

Something to keep in mind with both of these is that you are always doing a comparison - in the case of Corsi Rel you are comparing a player, and his line, to the performance of his teammates when he is off the ice. If you have two equally skilled fourth liners, the one playing for Detroit or St. Louis will have a much worse Corsi Rel than the one playing in Minnesota or Nashville because the players in the comparison group are much better.

WOWY is the same way - Crosby's results without Dupuis depend on who tends to slot in when Dupuis is injured or shifted to another line. Keep in mind that you are always comparing a player's performance to some specific group of teammates. This is important if his team is very strong or weak at the same position or if you are using one of these to compare players on different teams.

In the next installment, I will look at a couple methods that get around this by assessing everyone at once - regression and Vic Ferrari's King Value.